Can you get Unity to ignore the second touch?

You can tell how many touches are detected in a given frame by checking the Input.touchCount property. So, you could just wrap your "move" code with something like;

 if (Input.touchCount == 1) 
 {
     // Only 1 touch active here, so do 1-touch motion...
 }

For handling a single touch; this will help:

 void Update ()
 {
 
     // ... some other code ....
 
     if (Input.touchCount > 0)
     {
         switch (Input.GetTouch(0).phase) {
         case TouchPhase.Began:
             // code to run when touch begins here...
             break;
         case TouchPhase.Moved:
         case TouchPhase.Stationary:
             // code to run when touch is being dragged here...
             break;
         case TouchPhase.Ended:
             // code to run when touch is lifted up and finished here...
             break;
         case TouchPhase.Canceled:
             // code to run when touch is interrupted and does not get to run the 'Ended' case here... (jumps from dragging to being canceled by some interruption like a phone call)
             break;
         }
     }
 
     // ... Some other code ...
 
 } // end Update

if you want to handle multiple touches, just change the IF to a FOR loop [ for (int i = 0; i < Input.touchCount; i++) ] and instead of directly using getTouch(0) use getTouch (i).

Hope its useful.